Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral.
∫(3y⁴+6y²-1)/(y³+2y)dy
Perform long division on the given"

A. ∫(3y-2)dy + ∫(4y²+8)dy - ∫(5y⁻¹)dy
B. ∫(3y-2)dy + ∫(4y²+8)dy + ∫(5y⁻¹)dy
C. ∫(3y-2)dy - ∫(4y²+8)dy + ∫(5y⁻¹)dy
D. ∫(3y-2)dy - ∫(4y²+8)dy - ∫(5y⁻¹)dy